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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 27380.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27380.c1 | 27380d3 | \([0, 1, 0, -56585, -5198600]\) | \(488095744/125\) | \(5131452818000\) | \([2]\) | \(77760\) | \(1.4248\) | |
27380.c2 | 27380d4 | \([0, 1, 0, -49740, -6496412]\) | \(-20720464/15625\) | \(-10262905636000000\) | \([2]\) | \(155520\) | \(1.7714\) | |
27380.c3 | 27380d1 | \([0, 1, 0, -1825, 20028]\) | \(16384/5\) | \(205258112720\) | \([2]\) | \(25920\) | \(0.87551\) | \(\Gamma_0(N)\)-optimal |
27380.c4 | 27380d2 | \([0, 1, 0, 5020, 140500]\) | \(21296/25\) | \(-16420649017600\) | \([2]\) | \(51840\) | \(1.2221\) |
Rank
sage: E.rank()
The elliptic curves in class 27380.c have rank \(1\).
Complex multiplication
The elliptic curves in class 27380.c do not have complex multiplication.Modular form 27380.2.a.c
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.